New York State Attorney General Letitia James addressing media outside the U.S. Supreme Court on April 23, 2019.

After being armed with subpoena power from a formal referral Monday, New York Attorney General Letitia James is now tasked with picking an outside law firm to investigate the sexual harassment claims against Gov. Andrew Cuomo.

No law firm has been unveiled, but the selectee will be assigned a high-profile, closely watched investigation that could have deep political and governing implications for one of the most powerful governors in the United States.

The very selection of a law firm could have consequences for the investigation overall: A law firm too close to the governor's network or state business could taint the results in the public eye.

"The AG must avoid the appearance of impropriety, e.g., the selection will not have ever been involved in the defense of the State," read a statement from the Sexual Harassment Working Group, which is comprised of former state legislative staffers who have reported or experienced sexual harassment.

"This calls for a true neutral," they said. 

Under a barrage of disapproval from Democrats at various levels, the governor's public profile is plummeting after two former aides accused him of sexual harassment. 

There are growing calls for Cuomo to resign after a third woman came forward to accuse him of inappropriate behavior. Anna Ruch told the New York Times the governor touched her back and her face moments after meeting at a wedding reception and asked to kiss her.

An official with the Cuomo administration did not immediately respond to a request for comment.

Ruch's story comes after former aide Charlotte Bennett came forward with accusations that Cuomo quizzed her on her sex life and her views on relationships with older men.

Bennett, who is in her mid 20s, told the Times that Cuomo asked about whether she'd had sex with older men and if she was monogamous in relationships. 

Lindsey Boylan, another former aide, went public with detailed accusations against Cuomo last week in an online essay.

In an online essay, Boylan accused Cuomo of kissing her on the lips without her permission at his New York City office and said he once suggested they play strip poker. Cuomo's office has denied Boylan's allegations.

Finding the right law firm for the attorney general's investigation will be made more difficult with Cuomo's vast network of contacts as governor, said Blair Horner, executive director of the New York Public Interest Research Group.

"You might be looking for a legal unicorn," he said, also noting the governor's ties to New York's legal community.

The selected law firm should have unimpeachable qualifications and be able withstand public scrutiny, Horner said. They should not have a direct conflict of interest with Cuomo, but a distant connection to the governor's network might not be an automatic disqualification, he said.

There's a wide array of ties between New York's sprawling state government and law firms. Some firms lobby or receive high-priced contracts from the state. Many lawyers also funnel money to political committees and interest groups.

Attorney Jeanne Christensen, who specializes in sexual harassment cases, said the outside law firm should have no ties to the governor and should have expertise in sexual harassment claims.

There are a limited number of attorneys who are skilled in that area of law, which likely narrows the field of potential candidates, she added.

The state attorney general's office could go outside of New York for someone who has little connection with the state's politics, she said.

"People in the top of this field practice all over the U.S.," she said.

Laurie Berke-Weiss, a labor and employment lawyer who handles sexual harassment cases, said the investigation should include talking to the accusers, people they spoke with at the time of the incident and any witnesses inside the governor's office. The inquiry, she said, could even lead investigators to interview Cuomo himself.

"It really has to be extremely thorough," she said.

Calls for Cuomo's resignation have come from U.S. Rep. Kathleen Rice and some lawmakers in the state Legislature.

The New York Working Families Party called for the third-term governor to resign as well.

"Andrew Cuomo's reign of fear, harassment, and intimidation cannot continue," said Sochie Nnaemeka, party state director, in a statement.

After the accusations from Bennett, the governor released a statement and contended that he never inappropriately touched anyone and never sought to make anybody feel uncomfortable. But Cuomo acknowledged he makes jokes at work and said he sometimes thinks he is "being playful." 

"I now understand that my interactions may have been insensitive or too personal and that some of my comments, given my position, made others feel in ways I never intended. I acknowledge some of the things I have said have been misinterpreted as an unwanted flirtation," he said in the statement, which has received criticism.